Physics problem. Please help.

Question

A bus starts from rest and accelerates at 1.5m/s^2 until it reaches a velocity of 9m/s. The bus continues at this velocity and then decelerates at -2m/s^2 until it comes to a stop 400m from its starting point. How much time did the bus take to cover 400 m.

Also I would like to know how you guys solve these kind of problems. Is it like thinking or just plugging it into a formula?

Answer 1

34.6 seconds.

Its a bit of both, it took me many steps so im gonna explain it logically:

First u find the time it takes till the final velocity reaches 15 m/s (6 seconds)

Then u calculate the time it take for a car to decelerate to a stop when its moving at 15 and is decelerating at 2 ms(squared) (7.5 seconds)

Afterwards u take the distance travelled in the 6 seconds and in the 7.5 seconds separately, then u sum it up and subtract it from 400 which leaves u with the distance the car moved at the speed of 15 m/s, u use the speed = distance/time formula and then u add the final answer for time (21.1 seconds)

So the total time = 34.6 seconds